How to view WebM video on your iPhone or iPad

Google's WebM video file format has become nichely popular in the years since its debut. As a royalty-free alternative to H.264 standard, it's used for high-quality-but-low-bandwidth videos on sites like YouTube, Reddit, 4chan, and the like. I'm not going to get into the reasons why people might prefer WebMs to gifs, MP4s, MKVs, or FLVs; frankly, I see it as a personal/site-specific preference. But here's the thing: those people who desperately want to view WebMs on their iPhone? They run into a bit of a snag when using a mobile web browser.
Because Apple's QuickTime player codec doesn't support WebM. That means no WebM videos in Safari, no WebM videos in Chrome (which uses the same WebKit-based rendering engine on iOS), no WebM videos in any third-party browser or any app integrating a web view.
But don't woe over WebM just yet: There's a third-party app to save you from your troubles.